PHYSICS-INFORMED NEURAL NETWORK APPROACH FOR IDENTIFICATION OF DYNAMIC SYSTEMS

Abstract

In this study, a novel method for online and real-time identification of dynamic systems is presented. This method is based on the newly introduced algorithm Physics Informed Neural Network (PINN). In order to find the dynamic characteristics of the system, sparse displacement measurements are fed to the Artificial Neural Network (ANN); By introducing the classic vibration equation of the system to the ANN as a physics constraint, the PINN estimates both dynamic characteristic and state of the system. The proposed framework is evaluated by several numerical studies with different system properties, noise levels, architecture, and training data. On that account, four structural systems are presented: (1) single-degree-of-freedom (SDOF) systems with different properties and noise levels, as basis model with an accurate analytical solution (2) a three-degree-of-freedom (3-DOF) system with both complete and sparse measurements, representing the structural model of the n-story shear frames (3) a simple supported beam subjected to an initial displacement with several NNs architecture and sensor numbers, and (4) a Pure Cubic Oscillator (PCO) as a nonlinear dynamic system. The results of the proposed platform for the PINN are compared to a mutual ANN in all cases to emphasize the superiority of the PINN in both determining the dynamic characteristics and state estimation of dynamic systems. In addition, the performance of both NNs is examined with different training data to ensure the resilience of the algorithm and affirm the role of the added criteria, physics constraint, in reducing the dependency on the training data. The proposed algorithm can accurately estimate the dynamic characteristics of different dynamic systems with sparse, noisy measurements; by means of the classic dynamic equations and smartly selection of the hidden layer numbers, the PINN will be a powerful predictive tool for the dynamic analysis in the absence of any prior knowledge of the dynamic systems.